which projects vectors in \(T \mathbb {R}^n\)  onto their component in \(TS_n\)  along the direction of \(\mathcal {N}\) , see Figure REF . This allows one to isolate components of the map contributing to dynamics in \(TS_n\) . The following result should be compared with the characterisation of the reduced problem in fast-slow ODEs presented in [1]}, see also [2]}, [3]}, [4]}, [5]}.
<FIGURE>